🦄 Orbital Shift: Rotate Array Right

Difficulty: Beginner Tags: arrays, math, modulo, slicing Series: CS 102: Problem Solving & Logic

Problem

In the mystical orbital realm, elements shift positions in a circular pattern. Your task is to rotate an array to the right by k steps.

Given an array nums and an integer k, rotate the array to the right by k steps. Each step moves every element one position to the right, with the last element wrapping around to the front.

Real-World Application

Array rotation appears in: - Circular buffers - ring buffers in audio/video processing - Time series data - shifting time windows for analysis - Image processing - rotating pixel data for transformations - Cryptography - Caesar cipher implementations - Game development - cycling through inventory items - Scheduling algorithms - round-robin task scheduling - Data compression - Burrows-Wheeler transform preprocessing

Input

data = {
    'nums': list[int],  # Array to rotate
    'k': int            # Number of steps to rotate right
}

Output

list[int]  # Rotated array

Constraints

• Array length ≤ 100,000
• k ≥ 0 (can be larger than array length)
• You may create a new array (in-place not required)

Examples

Example 1: Basic Rotation

Input: {'nums': [1,2,3,4,5,6,7], 'k': 3}

Output: [5,6,7,1,2,3,4]

Explanation: - Step 1: [7,1,2,3,4,5,6] - Step 2: [6,7,1,2,3,4,5] - Step 3: [5,6,7,1,2,3,4]

Or more simply: - Last 3 elements [5,6,7] move to front - First 4 elements [1,2,3,4] move to back

Example 2: k Larger Than Array Length

Input: {'nums': [1,2], 'k': 5}

Output: [2,1]

Explanation: - Array length = 2 - k = 5, so effective rotation = 5 % 2 = 1 - Rotate right by 1: [2,1]

Example 3: No Rotation

Input: {'nums': [1,2,3,4], 'k': 0}

Output: [1,2,3,4]

Explanation: - k = 0, no rotation needed

Example 4: Full Rotation

Input: {'nums': [1,2,3], 'k': 3}

Output: [1,2,3]

Explanation: - k = 3 = array length - Full rotation returns to original position

Example 5: Single Element

Input: {'nums': [1], 'k': 10}

Output: [1]

Explanation: - Single element array remains unchanged

Example 6: Empty Array

Input: {'nums': [], 'k': 5}

Output: []

Explanation: - Empty array remains empty

What You'll Learn

• Using modulo arithmetic to handle large k values
• Array slicing techniques in Python
• Understanding circular/cyclic operations
• The relationship between left and right rotations

Why This Matters

Array rotation is a classic interview problem that tests: - Index manipulation skills - Understanding of modulo arithmetic - Ability to optimize with mathematical insights - Edge case handling

Starter Code

def challenge_function(data):
    """
    Rotate array to the right by k steps.

    Args:
        data: dict with keys:
            - 'nums' (list[int]): array to rotate
            - 'k' (int): number of steps to rotate right

    Returns:
        list[int]: rotated array
    """
    # Your implementation here
    pass